Uniformites et Continuity Spaces
| dc.creator | Isidore, Fleischer | |
| dc.creator | Gaston, Giroux | |
| dc.date | 2008-11-17 | |
| dc.date.accessioned | 2026-07-07T10:18:53Z | |
| dc.date.available | 2026-07-07T10:18:53Z | |
| dc.description | A semigroup A is an abelian semigroup with identity 0. A set of positives in A is an ordered down-directed set P containing with every r an element r/2 with r/2 + r/2 = r. A continuity space is an abstract set X equipped with a map d : XxX to A satisfying d(x, x) = 0 and d(x, z) d(x, y) + d(y, z). A quasi-uniform space is an abstract set X equipped with a filterbase of binary relations {U} such that each U contains the diagonal as well as for some V{U}. For each rP, the set } is seen to be a quasi-uniform filterbase on X . Indeed, the down-directedness of P ensures that U(r) is a filterbase of oversets of the diagonal and U(r) contains U(r/2)U(r/2). One obtains a uniform filterbase by symmetrization, i.e. by intersecting the U(r) with the U(s) = {(y, x)|d(y, x) <s}. | |
| dc.identifier | https://arxiv.org/abs/0811.2738 | |
| dc.identifier | http://arxiv.org/abs/0811.2738 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174342 | |
| dc.subject | General Topology | |
| dc.title | Uniformites et Continuity Spaces | |
| dc.type | text |